Question: Solve for $x$ : $10\sqrt{x} + 1 = 7\sqrt{x} + 9$
Solution: Subtract $7\sqrt{x}$ from both sides: $(10\sqrt{x} + 1) - 7\sqrt{x} = (7\sqrt{x} + 9) - 7\sqrt{x}$ $3\sqrt{x} + 1 = 9$ Subtract $1$ from both sides: $(3\sqrt{x} + 1) - 1 = 9 - 1$ $3\sqrt{x} = 8$ Divide both sides by $3$ $\frac{3\sqrt{x}}{3} = \frac{8}{3}$ Simplify. $\sqrt{x} = \dfrac{8}{3}$ Square both sides. $\sqrt{x} \cdot \sqrt{x} = \dfrac{8}{3} \cdot \dfrac{8}{3}$ $x = \dfrac{64}{9}$